Question

A manufacturing company constructs a 1-cm assembly by snapping together four parts that average 0.25 cm in length. The company would like the standard deviation of the length of the assembly to be 0.01 cm. Its engineer, Peter Purdue, believes that the assembly will meet the desired level of variability if each part has standard deviation 0.01/4 = 0.0025 cm. Instead, show Peter that you can do the job by making each part have standard deviation 0.01/4 = √0.005 cm. This could save the company a lot of money because not as much precision is needed for each part.